Conventional elevators have a counterweight and an elevator car each traveling vertically guided along two guide rails. The counterweight guide rails extend typically vertically on opposite sides of the counterweight. The plane on which the two guide rails of the counterweight are positioned is called the guide rail plane of the counterweight. The elevator car is typically connected to a counterweight with a suspension roping. This roping may be connected to the counterweight either by fixing an end of the roping to the counterweight or by guiding the roping around one or more pulleys mounted on the counterweight. In the latter case, the pulley is mounted on upper part of the counterweight frame, for instance on the cross beam. In that case, the pulley has been mounted via a pulley frame which is fixed on the cross beam that connects the side structures of the counterweight frame. In some cases, the roping must be guided to pass to and from the counterweight pulley on a route that requires the pulley positioned such that its plane of rotation is an acute angle (e.g. between 5-20 degrees) relative to the guide rail plane. This may be needed because of numerous various reasons. Often this is needed to achieve good space efficiency. For instance, the roping may need to pass adequately far apart from other elevator components. Also, it may be necessary to guide the ropes in this way so as to suspend the elevator car in a particular way. A problem in known arrangements has been that the shape of the cross beam has been complicated and due to the angle between the rotation plane and the cross structure additional stiffeners have been necessary. Both the shape and number of parts adds to the cost of the product. Also, the complicated structure has made it difficult to get access to the pulley for maintenance. Additionally, it has been noticed that the different alignment of the cross beam of the frame and the pulley has causes that the frame tends to twist around a vertical axis and lean excessively on the guide rails via its guide members, such as the guide rollers or the guide sliders. This twist has the drawback that it increases the noise level and wear of the guide members.